Pricing interest rate guarantees in a defined benefit pension system

Abstract

In Norwegian defined benefit pensions, assets corresponding to the premium reserve and premium fund are guaranteed a minimum return of a fixed rate r. This r is the same interest rate used for discounting when calculating the premium reserve. The guarantee is issued by the insurance company to each client. In this paper we aim at pricing an interest rate guarantee which is given by a put option with a stochastic strike depending on events in the membership data. We want to consider a complete and an incomplete asset market model with respect to this put option with an underlying given by the client assets and buffer funds. A risk indifferent pricing principle will be applied in the incomplete case, and results from this will be compared with Black and Scholes prices in the complete case.